Quadratic Roots Calculator

Solve ax² + bx + c = 0 with the quadratic formula: see the discriminant and both real roots, or learn when the roots are complex.

Calculator

Discriminant1
x13
x22

Method and variables

Quadratic Roots Calculator

Formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a

  • a, b, c — coefficients in ax^2 + bx + c = 0

Assumption: The coefficient a cannot be zero.

Worked example

Quadratic Roots Calculator

For x^2 - 5x + 6 = 0, the roots are 2 and 3.

Important limits

  • Quadratic Roots Calculator: The current tool reports real roots only; a negative discriminant has complex roots.